@article{bernuauRobustFinitetimeOutput2015,
  title = {Robust Finite-Time Output Feedback Stabilisation of the Double Integrator},
  author = {Bernuau, Emmanuel and Perruquetti, Wilfrid and Efimov, Denis and Moulay, Emmanuel},
  date = {2015-03-04},
  journaltitle = {International Journal of Control},
  shortjournal = {Int. J. Control},
  volume = {88},
  number = {3},
  pages = {451--460},
  issn = {0020-7179, 1366-5820},
  doi = {10.1080/00207179.2014.956340},
  url = {http://www.tandfonline.com/doi/abs/10.1080/00207179.2014.956340},
  urldate = {2024-03-07},
  langid = {english},
  keywords = {双积分},
  file = {C:\Users\jinze\Zotero\storage\NXBKCX53\Bernuau 等 - 2015 - Robust finite-time output feedback stabilisation of the double integrator.pdf}
}

@incollection{orlovExtendedInvariancePrinciple2006,
  title = {Extended Invariance Principle and Other Analysis Tools for Variable Structure Systems},
  booktitle = {Advances in {{Variable Structure}} and {{Sliding Mode Control}}},
  author = {Orlov, Yuri},
  editor = {Edwards, Christopher and Fossas Colet, Enric and Fridman, Leonid},
  date = {2006},
  series = {Lecture {{Notes}} in {{Control}} and {{Information Science}}},
  pages = {3--21},
  publisher = {Springer},
  location = {Berlin, Heidelberg},
  doi = {10.1007/11612735_1},
  url = {https://doi.org/10.1007/11612735_1},
  urldate = {2024-03-08},
  abstract = {Analysis and synthesis of Variable Structure Systems (VSS’) have attracted considerable research interest in the last decades. Although the existing literature on this subject includes numerous monographs and papers such as [2, 6, 9, 13, 15, 20, 30, 32], to name a few, these systems are far from being fully understood. In the present chapter, analysis tools for VSS’ are developed within the framework of methods of non-smooth Lyapunov functions with non-positive time derivatives along the system trajectories.},
  isbn = {978-3-540-32853-7},
  langid = {english},
  file = {C:\Users\jinze\Zotero\storage\YIQY83G8\11612735_1.pdf}
}

@article{suRobustFinitetimeOutput2015,
  title = {Robust Finite-Time Output Feedback Control of Perturbed Double Integrator},
  author = {Su, Yuxin and Zheng, Chunhong},
  date = {2015-10},
  journaltitle = {Automatica},
  shortjournal = {Automatica},
  volume = {60},
  pages = {86--91},
  issn = {00051098},
  doi = {10.1016/j.automatica.2015.07.008},
  url = {https://linkinghub.elsevier.com/retrieve/pii/S0005109815002848},
  urldate = {2024-03-07},
  abstract = {This paper addresses the problem of finite-time output feedback stabilization for the perturbed double integrator system. A simple output feedback proportional–derivative (PD) controller is proposed. Global finite-time stability is proven based on Lyapunov stability theory and geometric homogeneity technique. Furthermore, it is proven that the proposed controller can maintain local finite-time stability regardless of some nonlinear perturbations. Thus, the proposed controller actually can be applied to a large class of uncertain second-order nonlinear systems. Simulations demonstrate the effectiveness of the proposed approach.},
  langid = {english},
  keywords = {双积分},
  file = {C:\Users\jinze\Zotero\storage\2L46J6MV\Su和Zheng - 2015 - Robust finite-time output feedback control of perturbed double integrator.pdf}
}

@article{zavala-rioContinuousFinitetimeStabilization2022,
  title = {On the Continuous Finite-Time Stabilization of the Double Integrator},
  author = {Zavala-Río, Arturo and Sanchez, Tonametl and Zamora-Gómez, Griselda I.},
  date = {2022-04},
  journaltitle = {SIAM Journal on Control and Optimization},
  shortjournal = {SIAM J. Control Optim.},
  volume = {60},
  number = {2},
  pages = {699--719},
  issn = {0363-0129, 1095-7138},
  doi = {10.1137/20M136459X},
  url = {https://epubs.siam.org/doi/10.1137/20M136459X},
  urldate = {2024-03-07},
  abstract = {Continuous finite-time stabilization is often treated under the analytical framework of homogeneity and has been frequently illustrated in the context of the feedback control of the double integrator. For such a simple system, the simplest considered continuous finite-time controller is composed of gained (proportional) exponentially weighted position and velocity error correction terms, with the exponential weights generally less than unity and constrained to satisfy a particular relation among them under homogeneity. What happens for less-than-unity exponential weights that do not satisfy such a homogeneity-based relation? Does the finite-time stabilization hold? Through a Lyapunov function--based study, we analyze and give more concrete answers to such questions than those partially provided by previous studies on the topic. We do find a more exhaustive spectrum of the exponential weights that give rise to finite-time stability of the trivial solution. Other types of stability properties are further found to take place for less-than-or-equal-to-unity exponential weights. Moreover, through complementary analysis, local or ultimate behavior of the system solutions is further characterized. The analytical findings are further illustrated through computer simulations.},
  langid = {english},
  keywords = {双积分},
  file = {C:\Users\jinze\Zotero\storage\SL6Y4W5A\Zavala-Río 等 - 2022 - On the Continuous Finite-Time Stabilization of the Double Integrator.pdf}
}

@book{shtesselSlidingModeControl2014,
  title = {Sliding Mode Control and Observation},
  author = {Shtessel, Yuri and Edwards, Christopher and Fridman, Leonid and Levant, Arie},
  date = {2014},
  series = {Control {{Engineering}}},
  publisher = {Springer New York},
  location = {New York, NY},
  doi = {10.1007/978-0-8176-4893-0},
  url = {http://link.springer.com/10.1007/978-0-8176-4893-0},
  urldate = {2023-12-27},
  isbn = {978-0-8176-4892-3 978-0-8176-4893-0},
  langid = {english},
  file = {C:\Users\jinze\Zotero\storage\J6RF6BG6\Shtessel 等 - 2014 - Sliding Mode Control and Observation.pdf}
}

@article{orlovFiniteTimeStability2004,
  title = {Finite Time Stability and Robust Control Synthesis of Uncertain Switched Systems},
  author = {Orlov, Y.},
  date = {2004-01},
  journaltitle = {SIAM Journal on Control and Optimization},
  shortjournal = {SIAM J. Control Optim.},
  volume = {43},
  number = {4},
  pages = {1253--1271},
  issn = {0363-0129, 1095-7138},
  doi = {10.1137/S0363012903425593},
  url = {http://epubs.siam.org/doi/10.1137/S0363012903425593},
  urldate = {2024-04-11},
  abstract = {Stability analysis is developed for uncertain nonlinear switched systems. While being asymptotically stable and homogeneous of degree q {$<$} 0, these systems are shown to approach the equilibrium point in finite time. Restricted to second order systems, this feature is additionally demonstrated to persist regardless of inhomogeneous perturbations. Based on this fundamental property, switched control algorithms are then developed to globally stabilize uncertain minimum phase systems of uniform m-vector relative degree (2, . . . , 2)T . The controllers constructed do not rely on the generation of sliding motions while providing robustness features similar to those possessed by their sliding mode counterparts. The proposed synthesis procedure is illustrated via application to a friction servo-motor.},
  langid = {english},
  file = {C\:\\Users\\jinze\\Zotero\\storage\\5E8DWH8V\\Orlov - 2004 - Finite time stability and robust control synthesis of uncertain switched systems.pdf;C\:\\Users\\jinze\\Zotero\\storage\\5TZJVPQF\\Orlov - 2004 - Finite time stability and robust control synthesis of uncertain switched systems.pdf}
}
